A Nomogram for Chi-Square
卡方概率列线图AI 解读 ↓
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卡方概率列线图
- 研究问题
- 如何通过图形工具，根据卡方统计量和自由度读取上尾概率，并处理常用概率表覆盖范围之外的统计量组合？
- 方法与思路
- 所给文本介绍三刻度列线图：连接统计量与自由度刻度，在概率刻度读取结果，并通过示例及查表结果比较读数。
- 材料陈述的贡献
- 文本称列线图能实现常用卡方表的查询功能，并覆盖更高统计量和自由度；还提到针对一个自由度的读数精度比较。
- 阅读关注点
- 应查看列线图原图的刻度、覆盖范围与读取操作，并核对精度比较表，判断不同概率区域的图形读数误差。
- 阅读边界
- 所给OpenAlex索引文本未注明稿件版本，且没有附图和精度表；不能仅据示例判断全范围精度，需查原PDF。
原文摘要
T O DECIDE if a calculated value of x2 is significant it is customary to use a table such as that given by Fisher [5]. The experimenter thus finds the frequency with which, according to some hypothesis as to the population(s) from which the samples are drawn, random sampling would give numbers leading to a x2 greater than that actually obtained. Presently available tables may give values of this probability for integral values of x2 (Elderton, Yule), or, as in Fisher's table, values of x2 for selected values of the probability. The results obtained with either type of table can be obtained by use of the attached nomogram or alignment chart (Figure 1). If an index line, such as a stretched thread or a line ruled on some flat transparent material is used to connect the calculated values of x2 on the right-hand scale with the appropriate number of degrees of freedom (DF) on the middle scale, the point at which the index line crosses the left-hand scale gives the value of the probability (P). Example: Suppose we have calculated a value of x2 = 9.837 for three degrees of freedom. Connecting these values on the appropriate scales of the nomogram by the index line, we read on the left-hand scale P = 0.020. From Fisher's Table III we also find 0.020. For the frequently occurring and important case of one degree of freedom, the degree of accuracy to be expected from the nomogram is shown by Table 1, where readings from the nomogram are compared with the correct probabilities as given on p. 445 of Kendall [7]. The nomogram contains higher values of x2 and DF than found in most tables, enabling cases in which such values occur to be treated directly without any approximate calculations. Example: A value of x2=64 corresponding to DF =41 has been found. From the nomogram, P=0.0103. Yule and Kendall [8], on p. 459, give P=0.0103.